Unsolved problems in number theory

By András Sárközy. Periodica Mathematica Hungarica, 2001

1,013 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/2aebdc0a90b476551a10a258279649e73a043379

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

In Electrical and Electronic Engineering

Citations in the corpus

Wolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862--2012) (2011, background): “[39] R.K. Guy, Unsolved problems in Number Theory, Third edition, Springer-Verlag, New York, 2004.”
COUNTING THE NUMBER OF SOLUTIONS TO THE ERDŐS–STRAUS EQUATION ON UNIT FRACTIONS (2011, methodology): “The Erdős–Straus conjecture (see for example [24]) asserts that f (n) > 0 for all n > 2; it remains unresolved, although there are a number of partial results.”
Sieving by large integers and covering systems of congruences (2005, background): “Examples with distinct moduli are known with least modulus 2, 3, and 4, where this reciprocal sum can be arbitrarily close to 1; see [10], §F13.”
How is ChatGPT's behavior changing over time? (2023, background): “To further investigate ChatGPT’s math problem-solving and chain-of-thought behaviors, we asked it to tackle a different math problem: counting the number of happy numbers (Guy, 2004, pp. 357-360) within a given interval.”
When is the Fourier transform of an elementary function elementary? (2000, background): “there is no known simple necessary and suﬃcient condition for the existence of an exact covering system, and various questions about exact covering systems are the subject of an extensive theory (see [6], problem F14, 24 and references therein). It is interesting, therefore, that in a special case, ”
Ramsey Theory on the Integers (2014, background): “Examples include Old and New Problems and Results in Combinatorial Number Theory [92] by Erdős and Graham, Unsolved Problems in Number Theory [135] by Guy, and The New Book of Prime Number Records [220] by Ribenboim.”
Fibonacci and Lucas numbers with applications (2002, neutral): “Guy of the University of Calgary, Alberta, Canada, in his fascinating book, Unsolved Problems in Number Theory [254], presents an interesting number sequence {xn}.”